OR_Tomorrow.docx - GA1 LP SA u2013 3.12 3.13 3.28 3.32,4.2...

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GA1 LP & SA – 3.12 & 3.13, 3.28, 3.32,4.2, 4.10 CHAPTER 3 3.12. Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production requirements per unit are as follows: For the coming production period, the company has 200 fan motors, 320 cooling coils, and 2400 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: The computer solution is shown in Figure 3.17. a. What is the optimal solution, and what is the value of the objective function?
b. Which constraints are binding?
c. Which constraint shows extra capacity? How much?
d. If the profit for the deluxe model were increased to $150 per unit, would the optimal solution change? Use the information in Figure 3.17 to answer this question.
3.13 . Refer to the computer solution of Problem 12 in Figure 3.17. a. Identify the range of optimality for each objective function coefficient.
b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal solution be?
c. Identify the range of feasibility for the right-hand-side values.
d.If the number of fan motors available for production is increased by 100, will the dual value for that constraint change? Explain.
3.28 The Pfeiffer Company manages approximately $15 million for clients. For each client, Pfeiffer chooses a mix of three investment vehicles: a growth stock fund, an income fund, and a money market fund. Each client has different investment objectives and different tolerances for risk. To accommodate these differences, Pfeiffer places limits on the percentage of each portfolio that may be invested in the three funds and assigns a portfolio risk index to each client.

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